High-Order Time-Stable Numerical Boundary Scheme for the Temporally Dependent Maxwell Equations in Two Dimensions

High-order time-stable boundary operators for perfectly electrically conducting (PEC) surfaces are presented for a 3×3 hyperbolic system representing electromagnetic fields TE to z. First a set of operators satisfying the summation-by-parts property are presented for a 2×2 hyperbolic system representing one-dimensional electromagnetic propagation in a PEC cavity. Boundary operators are then developed for two-dimensional electromagnetic propagation in the xy-plane. This procedure leads to a time-stable scheme for a 3×3 hyperbolic system and concurrently shows how to eliminate the ambiguity associated with tangential and normal electromagnetic field components at corners and edges of PEC scatterers when using colocated computational electromagnetic schemes. A numerical comparison to the popular Yee scheme is included, and this comparison suggests that the fourth-order (in space and time) scheme derived herein does effectively compute the Maxwell equations in two dimensions.